7/3x+1-x=19

Solution for 7/3x+1-x=19 equation:

7/3x+1-x=19

We move all terms to the left:

7/3x+1-x-(19)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/3x-18=0

We multiply all the terms by the denominator


-1x*3x-18*3x+7=0

Wy multiply elements

-3x^2-54x+7=0

a = -3; b = -54; c = +7;
Δ = b2-4ac
Δ = -542-4·(-3)·7
Δ = 3000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-10\sqrt{30}}{2*-3}=\frac{54-10\sqrt{30}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+10\sqrt{30}}{2*-3}=\frac{54+10\sqrt{30}}{-6}
$